Behaviour of Cold-Formed Steel Built-up I Section Under Bending

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1 Behaviour of Cold-Formed Steel Built-up I Section Under Bending Sudha.K #1, Sukumar. S #2 # Department of Civil Engineering, Government College of Engineering, Salem, Tamil Nadu, India 1 sudhajaikishan@gmail.com 2 sukumar_237@yahoo.co.in Abstract - This paper presents an experimental and numerical investigation on the bending strength and behaviour of cold-formed (CF) steel built-up flexural members. Eight specimens in two groups, first group of four specimens with equal flanges and second group of four specimens with unequal flanges have been fabricated and experimented. The experimental results show the modes of buckling and their influence on the bending strength and behaviour of CF built-up I sections. The experimental results are also verified by simulating finite element models and analysed using FEM software ANSYS. The results obtained are in good agreement with the experimental results. Keywords - Cold-formed Built-up section, Thin walled beam, Local buckling, Flexural behaviour, Distortional buckling, Crippling I. INTRODUCTION Cold formed steel products are extremely used in building industry and range from purlins to roof sheeting and floor decking. These sections are extensively used in various engineering applications because of their high strength to weight ratio. Thin walled I sections are preferred mostly due to their light weight and full strength capacity. Vlassov[1] presented the classical theory in this field excellently. Reviewing the present state of art one should mention the books presented by Bleich[2],Timoshenko[3], and Murray[4], in addition to a large number of papers based on linear analysis. Chajes[5], Yu[6], Bulson[7], Hancock[9], Pekoz [1,11] presented many papers on the stability of open cross-sections with solid webs. Based on the equilibrium at the deflected position of a structure Ganapathy Chettiar and Varghese[8] have developed a method to find the lateral buckling load of open-web frames and girders of any geometry and any support conditions. An experimental study on I- beams with slender sections has been carried out by Kubo and Fukumoto[12] and presented the interaction behaviour of local and lateral-torsional buckling in the inelastic buckling range. They also found that the beams with intermediate length undergo combined local and lateral-torsional buckling whereas the long beam fails only by lateral-torsional buckling. Put, Pi and Trahair[13] conducted lateral buckling strength tests on C and Z beams and summarized that local or distortional buckling occurs in the compression element. Yu and Schafer[15] presented the testing plan to restrict distortional buckling and a simple method to generate local buckling in C and Z beams. Yu and Schafer[18] presented another method to generate distortional buckling in cold formed steel C and Z beam and they also found that large strength reduction occurs as the distortional buckling is initiated instead of local buckling. In case of latticed steel members, as a bar with circular cross-section is very stiff torsionally and flexurally and as the full section of the bar is continuous at the joints where they are also welded, the system of web bars provides a high torsional and flexural stiffness at joints. In this, the load transmission relies solely on the weld connection, resulting in a discontinuous load-transfer mechanism. Heavy stress concentration is induced at the welded locations. Though many studies have been performed on buckling of cold formed steel profiles, few studies have been made on latticed / built-up cold-formed beams and remain largely unexplored. The literature on built up CF Sections are very minimum and are available for compression members[14,16,17]. Whereas the study on cold formed steel built up sections under bending is very rare. Hence in this investigation an attempt has been made to study the behaviour of CFS built up flexural members and to find the feasibility of such sections in the field of construction. Thin walled built-up I section beams are economical with same flexural rigidity when compared to thin walled solid web sections. Though this type of sections results in economic type of construction, presently the usage of such members are limited because of the complexity involved in the analysis and prediction of their behaviour become tedious. As this type of sections with open cross section are susceptible to multiple modes of buckling when they are connected together by a system of continuous bent bar with circular cross sections, the behaviour of the beam elements may be governed by local buckling in the component plates, distortional buckling of the outstanding legs and the local buckling of web element. ISSN : Vol 5 No 6 Dec 213-Jan

2 The Research activities presented in this current paper are focused on flexural behaviour of cold-formed steel latticed members under static lateral loading is a part of the ongoing research activity. This paper provides the outcome of the first experimental phase of the research devoted to study the behaviour of the latticed coldformed steel beams. II. TEST SPECIMEN Two types of built up CFS I Sections with equal and unequal flanges have been fabricated and experimented. The specimens are fabricated from 1.2mm thick steel sheets whose yield stress is 23 N/mm 2 and young s modulus of 1.98 x 1 5 N/mm 2. The specimens are built-up using four numbers of Cold Formed angles with lip in the flange alone. Out of four angles two are provided in the top flange and two at the bottom flange which act as the main chords of the member. These main chords are held in position by using a secondary member of 6mm diameter bar bent in the form of sinusoidal wave form of angle 45. The main chords and the secondary members are welded at the point of contact by spot welding. The cross section of the specimen is shown in the Fig.1 and the geometric properties of the section are tabulated in the Table 1. The series are designated as UEI top width thickness for unequal I sections and EI top width thickness for equal I sections. All the eight specimens were tested under two point loading. UEI is an unequal I section fabricated without stiffener under loading points so as to study the behaviour in bearing. EI Equal flange I sections were fabricated with 2mm thick stiffener plates to investigate the influence of bearing stiffeners. Other specimens were fabricated to study the local and distortional buckling of beams by strengthening the stiffeners against bearing failure. Two stiffener plates one on either side is provided at the points of loading and at the points of support. Fig. 1 Cross Section of the Specimen Table I Geometric Properties of the Sections S. Description (A) (B) (C) (L) (D) (ld) (tk ) No of Specimen mm mm mm mm mm mm mm 1. UEI UEI UEI UEI EI EI EI EI ISSN : Vol 5 No 6 Dec 213-Jan

III. EXPERIMENTAL INVESTIGATION The experimental work was conducted on a 5kN capacity self-straining frame.

Deflectometers were placed at three positions namely 1/3 rd distance, mid span and at support.

The load and corresponding deflection was observed. Loading was gradually applied till the specimen become unstable.

3 III. EXPERIMENTAL INVESTIGATION The experimental work was conducted on a 5kN capacity self-straining frame. The Specimens were experimented under simply supported end condition with two points loading. Deflectometers were placed at three positions namely 1/3 rd distance, mid span and at support. readings were taken in the top compression flange and in the lip of the compression flange. A Proving ring of 5kN capacity was used to measure the loading. The load and corresponding deflection was observed. Loading was gradually applied till the specimen become unstable. The procedure was repeated for all the eight specimens. The experimental set up is shown in Fig. 2. The modes of failure are noted for every specimen. Some of the tested specimens are shown from Fig. 3 to Fig. 6. The total critical moments, total ultimate moments and bending stress are presented in Table II. Fig. 2 Test Setup Fig. 3 Distortional Buckling Fig. 4 Wobbling of Bottom Web ISSN : Vol 5 No 6 Dec 213-Jan

5 4 2..5.1.15.2..1.1.2.2 Fig. 7(a) UEI 4 2.

4 Fig. 5 Local Buckling Fig. 6 Flexural Buckling Fig. 7(a) UEI 4 2. Fig. 7(b) UEI ISSN : Vol 5 No 6 Dec 213-Jan

5 Fig. 7(c) UEI 3 2. Fig. 7(d) EI Fig. 7(e) EI 3 2. Fig. 7(f) EI Fig. 7 Load Vs. Curves M/Mcr M/Mcr φ/φcr φ/φcr Fig. 8(a) UEI 4-2. Fig. 8(b) UEI ISSN : Vol 5 No 6 Dec 213-Jan

6 M/Mcr M/Mcr φ/φcr φ/φcr Fig. 8(c) EI 4 2. Fig. 8(d) EI 3 2. Fig. 8 Moment Vs. Curvature Curves Table II Experimental Results S. No. Description of Specimen Critical Moment knm Section Modulus mm 3 Critical Stress σ cr N/mm 2 Ultimate Moment knm Ultimate Stress σ ult N/mm 2 σ cr σ ult Mode of Failure 1. UEI B 2. UEI D 3. UEI F 4. UEI D 5. EI LS 6. EI F 7. EI L 8. EI L B Bearing Failure, D- Distortion, LS Local Buckling of Stiffener, F- Flexural Buckling, L Local Buckling IV. FEM ANALYSIS USING ANSYS An approximate idealised mid-line model with four noded shell 143 element, for plate and 3D element for lacing are chosen. A non linear analysis with large deflections on has been carried out. The model is force- loaded and the line search option is chosen for the analysis. All the sections fabricated for the experimental work (Table 1) were modelled and analysed. Failure mode shapes for some specimens are shown from Fig. 9 to Fig. 12 and the Critical moments and Ultimate moments are presented in Table 3. ISSN : Vol 5 No 6 Dec 213-Jan

7 Fig. 9 Wobbling in Web Fig. 1 Local Buckling Fig. 11 Distortional Buckling ISSN : Vol 5 No 6 Dec 213-Jan

Fig. 12 Distortional Buckling Table III Comparison of Experimental and ANSYS results S. No. Description of Specimen Total Critical Moment (knm) Exp ANSYS Total Ultimate Moment (knm) Exp ANSYS Exp.

8 Fig. 12 Distortional Buckling Table III Comparison of Experimental and ANSYS results S. No. Description of Specimen Total Critical Moment (knm) Exp ANSYS Total Ultimate Moment (knm) Exp ANSYS Exp. ANSYS Exp. ANSYS 1. UEI UEI UEI UEI EI EI EI EI V. RESULTS AND DISCUSSION The failure models are mixed bearing, local, distortional and flexural. The experimental failure modes are in good agreement with ANSYS results. Load Vs. Deflection curve shows that both exp and ansys are in good agreement. Bearing failure occurred in UEI under the loading points followed by local buckling of the elements of top chord members. EI series failed by buckling of stiffeners followed by mixed local and distortional bucking of compression chords. Wobbling effect as a sine wave is found in all the unstiffened elements (Lip and web elements). In the compression zone, the individual top chord members were distorted. UEI series failed by mixed local and distortional buckling of the individual chords. Equal Flange I-section carried approximately 4% more than that of unequal flange I section. The comparison shows that member strength is closely related to the failure pattern. For example the members (EI 4 2., UEI ) failed by flexural buckling exhibited higher bending stress closer to the yield stress and ultimate stress is reached as soon as the critical stress is reached, whereas those (EI 3 1.2, EI 3 2.) failed by local buckling in the lip and flange were unable to reach their yield stress. The members(uei-4-2., UEI-3-2.) failed by distortional buckling exhibited very low post buckling reserve strength, whereas those failed by local buckling (EI-4-1.2) showed high post buckling reserve strength. ISSN : Vol 5 No 6 Dec 213-Jan

9 Fig. 13 Load Vs Deflection Curve ( UEI 4-1.2) Fig. 14 Load Vs Deflection Curve ( UEI ) VI. CONCLUSIONS The experimental and numerical analyses on the bending strength and behaviour of cold-formed steel built-up I section flexural members have been investigated. The conclusions from the investigations are as follows It is observed that each chord member bend individually. This shows that this type of members does not bend in a single wave as a whole as in the case of solid cross- section, but the constituent members bend individually. The web element also contributing appreciably to the strength. Specimen failed under distortional buckling have little post buckling reserve strength whereas specimen failed under local or bearing have more post buckling reserve strength. To avoid bearing failure vertical stiffeners are required at support and at the loading points. By stiffening the web element of each chord member the capacity of the beam is further improved. Local buckling, distortional buckling and interaction between local and distortional buckling were observed. The FEA predictions are generally in good agreement with the experimental buckling modes. The results show that the buckling mode has greater influence on the strength of the specimens. ISSN : Vol 5 No 6 Dec 213-Jan

10 The comparison between the experimental results and the FEA predictions prove that the finite element analysis is a reliable tool to get quite accurate results in a reasonable amount of time. So the parametric study can be performed by the FEA to investigate the behaviour of Cold Formed Steel built up sections. REFERENCES [1] Vlasov. V.Z, Thin Walled Elastic Beams, Jerusalem, Israel: Israel Program for Scientific Translation,1961. [2] Bleich. F., Buckling Strength of Metal Structures, New York : McGraw-Hill Book Co., [3] Timoshenko. S.P. and Gere, J.M., Theory of Elastic Stability, New York : McGraw-Hill Book Co.,Inc., [4] Murray, N.W., Introduction to the theory of Thin-Walled Structures, London: Oxford University Press,1984. [5] Alexander Chajes, M., Principles of Structural Stability Theory, New Jersey: Prentice-Hall, Inc., Englewood Cliffs, [6] Yu, W.W., Cold-Formed Steel Design, New York : Wiley,2. [7] Bulson. P.S., The Stability of Flat Plates,London: Chatto and Windus,197. [8] Varghese P.C and Ganapathy Chettiar C. Lateral Stability of Plane Open Web Structures. Journal of Structural Engineering ASCE 1974; 1(ST11): [9] Hancock G.J. Local, Distortional and Lateral Buckling of I-Beams. Journal of Structural Engineering ASCE 1978; 14(11): [1] Reynand L.Serette, Teomen Pekoz Distortional Buckling of Thin-Walled Beams/Panels I: Theory. Journal of Structural Engineering ASCE 1995; 121(4): [11] Reynand L.Serette, Teomen Pekoz. Distortional Buckling of Thin-Walled Beams/Panels II : Design Methods. Journal of Structural Engineering ASCE 1995; 121(4): [12] Masahiro Kubo and Yuhshi Fukumoto. Lateral Torsional Buckling of Thin-Walled I Beams. Journal of Structural Engineering ASCE 1988; 114(4). [13] Bogdan M. Put, Yong-Lin Pi and Trahair N.S. Lateral Buckling Strength of Cold-formed Channel Section Beams. Journal of Structural Engineering, ASCE 1999; 125(11): [14] Sukumar. S, Parameswaran.P, Jayagopal L.S. Behaviour of built up open cross section under axial load. Journal of Structural Engineering ASCE 23; 3(4): [15] Cheng Yu and Benjamin W. Schafer Local Buckling Tests on Cold-Formed Steel Beams. Journal of Structural Engineering ASCE 23; 129(12): [16] Sukumar S, Parameswaran P and Jayagopal L.S. Torsional flexural buckling of built-up open cross sections under eccentric load. Journal of Structural Engineering ASCE 24; 3 (4): [17] Sukumar S, Parameswaran P and Jayagopal L.S. Local- Distortional- and Euler- buckling of thin walled built-up open cross sections under compression. Journal of Structural Engineering ASCE 26; 32(6): [18] Cheng Yu and Benjamin W. Schafer Distortional Buckling Tests on Cold-Formed Steel Beams. Journal of Structural Engineering ASCE 26; 132(4): ISSN : Vol 5 No 6 Dec 213-Jan

New approach to improving distortional strength of intermediate length thin-walled open section columns

New approach to improving distortional strength of intermediate length thin-walled open section columns R. S. Talikoti 1, K. M. Bajoria 2 1 Research Scholar (Email: rstalikoti@iitb.ac.in) 2 Associate Professor